Athermalized plastic lens

ABSTRACT

A plastic lens includes refractive and diffractive optical apparatus configured to produce optothermal changes substantially canceling each other over a predetermined working temperature range to render the plastic lens substantially athermalized over the range.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] The present application is a continuation-in-part of U.S.application Ser. No. 08/953,543, filed Oct. 20, 1997, which is acontinuation-in-part of U.S. application Ser. No. 08/624,935, filed Mar.22, 1996, which is a continuation-in-part of U.S. application Ser. No.08/173,255, filed Dec. 27, 1993, which is a divisional of U.S.application Ser. No. 07/860,390, filed Mar. 30, 1992. The fouraforementioned applications are incorporated by reference herein intheir entirety.

BACKGROUND OF THE INVENTION

[0002] The invention relates to an athermalized plastic lens.

[0003] In a system (e.g., a bar code scanner) that relies on a specificoptical property (e.g., a specific focal length) of a lens, changes intemperature that affect the specific optical property of the lens cancause the system to function improperly or inaccurately. For example, ifthe lens is used in a bar code scanner to focus light reflected from abar code symbol onto a CCD device that produces an image of the symbol,the produced image may be too out-of-focus to be effectively decoded ifthe focal length of the lens is affected significantly by a temperaturechange. Typically, a glass lens is more resistant to temperature changesthan a plastic lens having the same shape.

SUMMARY OF THE INVENTION

[0004] The invention provides an athermalized plastic lens in whichoptothermal changes are balanced by refractive and diffractive optics,allowing the lens to achieve thermal performance characteristics similarto those of a glass lens, while being inexpensive, lightweight, andeasily shaped. When the lens includes an axicon, the lens providesequipment such as bar code scanners with an extended working range.

[0005] Preferred implementations of the invention may include one ormore of the following. The lens may include a refractive surface and adiffractive optical element, wherein optothermal changes due to therefractive surface counter optothermal changes due to the diffractiveoptical element. The optothermal changes may cancel each other andinclude changes affecting the focal length of the lens. The lens mayinclude polycarbonate. The lens may include acrylic. The lens mayinclude a net positive power. The optothermal expansion coefficient ofthe refractive optical apparatus may be higher than an optothermalexpansion coefficient of the diffractive optical apparatus. The lens mayinclude a diffractive optical element that is substantially smaller thanthe lens. The first surface of the lens may provide substantially all ofthe negative power of the lens, and the second surface of the lens mayprovide substantially all of the positive power of the lens. The surfaceof the lens may provide substantially all of the negative power of thelens and substantially all of the positive power of the lens. Thediffractive optical apparatus may include a diffractive optical elementthat is substantially spherical in average. The surface of the lens maybe substantially flat. The refractive optical apparatus may be dividedunevenly between first and second surfaces of the lens. Substantiallyall of the diffractive optical apparatus may be disposed on one surfaceof the lens. The diffractive optical apparatus may be dividedsubstantially evenly between first and second surfaces of the lens. Thelens may include an axicon. The axicon may include a polymer. The axiconmay be disposed at a substantially spherical surface of the lens. Thediffractive optical element and the axicon may be disposed at differentsurfaces of the lens. The lens may include a diffractive optical elementthat includes at least eight phase levels. The lens may include adiffractive optical element that includes fewer than nine phase levels.The axicon may be affixed to a surface of the lens. The lens may includean aspherical surface having the optical properties of a combination ofa spherical surface with the axicon. The lens may include a doublet. Thelens may include a Cook triplet anastigmat. The lens may include asymmetric double Gaussian. The MTF of the lens may be higher with theaxicon than without the axicon for bar code symbols having spatialwavelengths of 10-20 mils, inclusive. The MTF of the lens may be atleast 0.2 for a 10 mil bar code symbol that is from about 4 to about 16inches away from the lens.

[0006] Other advantages and features will become apparent from thefollowing description and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 is an illustration of an embodiment of an athermalizedplastic lens having refractive surfaces and diffractive opticalelements.

[0008]FIGS. 2a and 2 b are illustrations of diffractive optical elementsthat are used in embodiments of the athermalized plastic lens.

[0009]FIGS. 3 and 4 illustrations of embodiments of the athermalizedplastic lens.

[0010]FIG. 5A is a conceptual illustration of an embodiment of theathermalized plastic lens having an axicon.

[0011]FIG. 5B is an illustration of the embodiment of FIG. 5A.

[0012]FIG. 6 is a flat-profile illustration of a diffractive opticalelement used in the embodiment of FIGS. 5A-5B.

[0013]FIG. 7 is an illustration of another embodiment of theathermalized plastic lens having an axicon.

[0014]FIG. 8 is an illustration of bar code scanning using anathermalized plastic lens having an axicon.

[0015]FIGS. 9A, 9B, 10A, 10B, 11A, and 11B show MTF curves forathermalized plastic lenses having different axicons.

[0016]FIGS. 12 and 13 show MTF curves for different spatial wavelengthsused with athermalized plastic lenses having different axicons.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017]FIG. 1 illustrates a lens 10 that is an embodiment of anathermalized plastic hybrid lens (“hybrid lens”) that includesrefractive and diffractive optics. As described below, by balancingchanges in optical properties resulting from temperature-inducedexpansion or contraction of lens material (“optothermal changes”), thehybrid lens achieves thermal performance characteristics similar tothose of a glass lens, while being inexpensive, lightweight, and easy toshape. The balancing is accomplished by special properties of surfacesand elements of the hybrid lens (e.g., spherical refractive surfaces 12,14 and diffractive optical elements (“DOEs”) 16, 18 of lens 10), asdescribed below.

[0018] In at least some cases, the optothermal changes resulting from atemperature change produce a focal length difference. For a particularlens, the nature of the relationship between the temperature change andthe focal length difference depends on the characteristics of the lens.In an athermalized lens, the temperature change produces no significantfocal length difference, i.e., the Focal length of an athermalized lensis not significantly affected by temperature changes.

[0019] Lens 10 has a focal length f that includes the followingcomponents that are related as described in equation (1) below: arefractive focal length f_(r) due to the refractive surfaces 12, 14which have focal lengths f_(r1) and f_(r2), respectively, and adiffractive focal length f_(d) due to the DOEs 16, 18 which have focallengths f_(d1) and f_(d2), respectively.

1/f=(1/f _(r1) +1/f _(d1))+(1/f _(r2) +1/f _(d2))=1/f _(r)+1/f _(d)  (1)

[0020] The refractive surfaces 12, 14 and DOEs 16, 18 have opto-thermalexpansion coefficients x_(r) and x_(d), respectively, each of which is ameasure of the extent to which the respective focal length (f_(r) orf_(d)) is changed per unit of temperature change. Equation (2) belowrelates changes Δf, Δf_(r), and Δf_(d) in focal lengths f, f_(r), andf_(d), respectively, to a temperature change ΔT. $\begin{matrix}{\frac{\Delta \quad f}{f} = {{{\frac{f}{f_{r}}\left( \frac{\Delta \quad f_{r}}{f_{r}} \right)} + {\frac{f}{f_{d}}\left( \frac{\Delta \quad f_{d}}{f_{d}} \right)}} = {\left( {{\frac{f}{f_{r}}x_{r}} + {\frac{f}{f_{d}}x_{d}}} \right)\Delta \quad T}}} & (2)\end{matrix}$

[0021] Since lens 10 is athermalized, focal length change Δf may betaken to be zero, to produce equation (3) which shows that in lens 10the ratio of expansion coefficient x_(r) to focal length f_(r) isbalanced by the ratio of expansion coefficient x_(d) to focal lengthf_(d). $\begin{matrix}{\frac{x_{r}}{f_{r}} = {- \frac{x_{d}}{f_{d}}}} & (3)\end{matrix}$

[0022] Solving equations (1) and (3) simultaneously produces equations(4a) and (4 b) which show that the ratio of coefficient x_(r) tocoefficient x_(d) and its inverse define relationships between focallength f and focal lengths f_(r) and f_(d), respectively.$\begin{matrix}\begin{matrix}{f_{r} = {\left( {1 - \frac{x_{r}}{x_{d}}} \right)f}} & \quad & \quad & {f_{d} = {\left( {1 - \frac{x_{d}}{x_{r}}} \right)f}}\end{matrix} & \left( {{4a},{4b}} \right)\end{matrix}$

[0023] For both the refractive surfaces and the DOEs, lens 10 may usepolycarbonate material, for which expansion coefficients x_(r) and x_(d)have the following values:

x _(r)=246(×10⁻⁶ ⁰ C ⁻¹)  (4c)

x _(d)=131(×10⁻⁶ ⁰ C ⁻¹)  (4d)

[0024] Equations (5a) and (5 b) below show that substituting thepolycarbonate coefficient values into equations (4a) and (4 b) producesa directly proportional relationship between focal length f and focallengths f_(r) and f_(d), respectively. $\begin{matrix}{f_{r} = {{\left( {1 - \frac{246}{131}} \right)f} = {{- 0.878}\quad f}}} & \left( {5a} \right)\end{matrix}$

$\begin{matrix}{f_{d} = {{\left( {1 - \frac{131}{246}} \right)f} = {0.467\quad f}}} & \left( {5b} \right)\end{matrix}$

[0025] Where lens 10 uses acrylic material, the following values andequations apply.

x _(r)=315(×10⁻⁶ ⁰ C ⁻¹)  (5c)

x _(d)=129(×10⁻⁶ ⁰ C ⁻¹)  (5d) $\begin{matrix}{f_{r} = {{\left( {1 - \frac{315}{129}} \right)f} = {{- 1.442}\quad f}}} & \left( {6a} \right) \\{f_{d} = {{\left( {1 - \frac{129}{315}} \right)f} = {0.591\quad f}}} & \left( {6b} \right)\end{matrix}$

[0026] Thus, where the hybrid lens has positive power (i.e., has a focallength greater than zero) and uses a material (e.g., polycarbonate oracrylic) for which refractive surfaces are more sensitive to temperaturechanges than DOEs (i.e., the value for coefficient x_(r) is greater thanthe value for coefficient x_(d)), the hybrid lens has the general shapeof a lens with negative power. However, in such a lens, the positivepower of the DOEs overcomes the negative power of the refractivesurfaces, to produce a net positive power For the lens. In at least somecases, such a lens can use DOEs that are small relative to the size ofthe lens.

[0027]FIGS. 2A and 2B illustrate lenses 20 and 22 of polycarbonate andacrylic, respectively, which lenses are other embodiments of the hybridlens and in each of which substantially all of the negative power of thehybrid lens is provided by one of the surfaces 12′ or 12″ andsubstantially all of the positive power is provided by another of thesurfaces 14′ or 14″.

[0028]FIG. 3 shows a lens 24 that is another embodiment of the hybridlens and in which one of the surfaces 12″″ provides not onlysubstantially all of the negative power but also substantially all ofthe positive power, and the other surface 14′″ provides no significantnegative or positive power. As shown in FIG. 3, the one surface mayinclude a DOE that is substantially spherical in average and the othersurface may be substantially flat and may be used for asphericalreplication.

[0029]FIG. 4 shows a lens 26 that is another embodiment of the hybridlens and in which one substantially spherical surface 12″″ provides lessof the refractive power than another substantially spherical surface14″″, and substantially all of the diffractive power is provided by asurface-relief DOE on the other substantially spherical surface 14″″.Surface 12″″ may have an aspherical surface or replica.

[0030] Where the two surfaces of the hybrid lens contributesubstantially equally to the diffractive power, a size increaseamounting to a factor of four may be achieved for features of the DOEswithout a significant loss in resistance to optothermal changes.

[0031] In at least some cases, because acrylic requires less refractiveand diffractive power than polycarbonate for the same focal length f asrevealed by equations (5a), (5 b), (6 a), (6 b) above, it may beadvantageous for the hybrid lens to be constructed of acrylic materialinstead of polycarbonate material.

[0032]FIG. 5B shows a lens 30 that is another embodiment of the hybridlens, which embodiment includes an aspherical mold that is pressed froma drop of polymer to form an axicon 32 on a substantially sphericalsurface 34 of the lens. The lens 30 also includes a DOE 36 formed inanother surface 38 of the lens. FIG. 5A provides a conceptualillustration of lens 30.

[0033] The DOE 36 may have eight phase levels 40 a-h as illustrated byFIG. 6 which for clarity shows DOE 36 in a flat profile, not in theactual convex profile provided in accordance with the athermal aspect ofthe hybrid lens as described above.

[0034] The axicon enhances the ability of the hybrid lens to focus laserbeams to achieve elongated profiles advantageous for bar-code scanning,as described below.

[0035]FIG. 7 shows a lens 42 that is another embodiment of the hybridlens, which embodiment has an aspherical surface 34′ that has theoptical properties of surface 34 combined with axicon 32. Thus lens 42performs similarly to lens 30 but is a single piece and therefore may beless expensive to manufacture.

[0036] Lenses 30 and 42 may be made of polycarbonate which hasproperties described above.

[0037] A lens-axicon combination may be particularly useful forextending the working range (e.g., by 50-100%) of a CCD-based bar codescanner. In the combination, the axicon operates as a phase correctionelement to allow the scanner to resolve an out-of-focus bar code thatthe scanner could not resolve by relying on the lens alone.

[0038]FIG. 8 illustrates lens 44 and axicon 46 which together are anexample combination 48 of the lens-axicon combination. Combination 48has an aperture 50 that has a diameter 1 and is a distance a from a CCDimager 52 of a bar code scanner, a distance b from an in-focus point 54,and a distance z from a barcode-bearing surface 58 at a surface point56. The lens 44 may be a doublet, a Cook triplet anastigmat or asymmetric double Gaussian, and provides optical power to bend incidentlight toward the imager 42. By providing a longitudinal sphericalaberration, the axicon 46 effectively elongates the focal depth of thelens 44 by contributing phase correction when the surface 58 is not atthe in-focus point 54. The axicon 46 has an axicon induced phasecoefficient α.

[0039] Equation (7) describes an MTF value as a function of spatialfrequency v (e.g., of a bar code symbol) for a lens having an axiconthat includes a circular pupil of diameter 1, and has polar coordinatevalues ρ and θ with an origin at the pupil's center, and a normalizedradial coordination value v (i.e., half of the product of ρ and diameter1), where λ represents the wavelength and λ represents the wave number(i.e., 2π divided by the wavelength λ). $\begin{matrix}{{{MTF}(\nu)} = {\frac{4}{\pi}{\int_{\theta = 0}^{\theta = {\pi/2}}{{\theta}\quad {\int_{r = 0}^{r = {{{- v}\quad \cos \quad \theta} + \sqrt{1 - {v^{2}\quad \sin^{2}\quad \theta}}}}{\cos \left\{ {k\left\lbrack {{4\quad v\quad r\quad \cos \quad \theta} + {\alpha \left( {\sqrt{v^{2} - {2v\quad r\quad \cos \quad \theta} + r^{2}} - \sqrt{v^{2} + {2\quad v\quad r\quad \cos \quad \theta} + r^{2}}} \right)}} \right\rbrack} \right\} r{r}}}}}}} & (7)\end{matrix}$

[0040]FIGS. 9A and 9B show modulation transfer function (“MTF”) curvesMTF1 a, MTF2 a, MTF3 a and MTF1 b, MTF2 b, MTF3 b, respectively, each ofwhich describes the sharpness of an image of a bar code symbol as afunction of the distance z, for a particular value (i.e., 0, −0.003, or−0.001) for the axicon induced phase coefficient α and a particularspatial wavelength (i.e., 10 mil or 20 mil) of the bar code symbol. Ahigh MTF value represents a substantially in-focus image at the imager,and an MTF value near zero represents an image that is almost completelyout of focus. In general, data can derived from an image of a bar codesymbol more accurately if the image is sharper.

[0041] As shown in FIG. 9A, where the spatial wavelength is 10 mil andthe axicon induced phase coefficient α has a value of 0 (i.e., wherethere is effectively no axicon), curve MTF1 a shows that the MTF valuepeaks at about 0.75 at a z distance of about 5 inches, and remains below0.2 for any z distance greater than 11 inches. By contrast, as shown bycurve MTF2 a, the use of an axicon having a value of −0.003 for theaxicon induced phase coefficient α changes the optical characteristicsof the lens-axicon combination so that the MTF value peaks at about 0.5at a z distance of about 9.5 inches, and remains above 0.2 in a zdistance range from about 4 inches to about 16 inches. Thus, forexample, if data can be derived accurately from a bar code symbol imagethat has a sharpness corresponding to an MTF value of 0.2 or greater,for a bar code symbol having a spatial wavelength of 10 mil the axiconallows data to be derived from a distance of up to about 16 inches,which is about 5 inches further than data can be derived without theaxicon.

[0042] FIGS. 9A, 10A-10B, and 11A-11B illustrate MTF curves MTF1 b-MTF3f for other values for the axicon induced phase coefficient α. FIGS. 12and 13 show other MTF curves that describe the sharpness of an image ofa bar code symbol as a function of a normalized spatial wavelength v forseveral values for the axicon induced phase coefficient α and severalvalues for focusing error w.

[0043] Other embodiments are within the scope of the following claims.For example, each lens may be formed from separate pieces (e.g.,refractive lens and DOE pieces) or may be formed as a single unit. Othertypes of plastic may be used. In each lens, refractive or diffractivepower may be distributed in any way that renders the lens substantiallyathermalized.

What is claimed is:
 1. A plastic lens, comprising: refractive anddiffractive optical apparatus configured to produce optothermal changessubstantially canceling each other over a predetermined workingtemperature range to render the plastic lens substantially athermalizedover the range.
 2. The lens of claim 1, comprising a refractive surfaceand a diffractive optical element, wherein optothermal changes due tothe refractive surface counter optothermal changes due to thediffractive optical element.
 3. The lens of claim 1, wherein theoptothermal changes canceling each other include changes affecting thefocal length of the lens.
 4. The lens of claim 1, comprisingpolycarbonate.
 5. The lens of claim 1, comprising acrylic.
 6. The lensof claim 1, wherein the lens has a net positive power.
 7. The lens ofclaim 1, wherein an optothermal expansion coefficient of the refractiveoptical apparatus is higher than an optothermal expansion coefficient ofthe diffractive optical apparatus.
 8. The lens of claim 1, comprising adiffractive optical element that is substantially smaller than the lens.9. The lens of claim 1, wherein a first surface of the lens providessubstantially all of the negative power of the lens, and a secondsurface of the lens provides substantially all of the positive power ofthe lens.
 10. The lens of claim 1, wherein a surface of the lensprovides substantially all of the negative power of the lens andsubstantially all of the positive power of the lens.
 11. The lens ofclaim 1, wherein the diffractive optical apparatus includes adiffractive optical element that is substantially spherical in average.12. The lens of claim 1, wherein a surface of the lens is substantiallyflat.
 13. The lens of claim 1, wherein the refractive optical apparatusis divided unevenly between first and second surfaces of the lens. 14.The lens of claim 1, wherein substantially all of the diffractiveoptical apparatus is disposed on one surface of the lens.
 15. The lensof claim 1, wherein the diffractive optical apparatus is dividedsubstantially evenly between first and second surfaces of the lens. 16.The lens of claim 1, wherein the lens includes an axicon.
 17. The lensof claim 16, wherein the axicon includes a polymer.
 18. The lens ofclaim 16, wherein the axicon is disposed at a substantially sphericalsurface of the lens.
 19. The lens of claim 16, wherein a diffractiveoptical element and the axicon are disposed at different surfaces of thelens.
 20. The lens of claim 16, comprising a diffractive optical elementthat includes at least eight phase levels.
 21. The lens of claim 16,comprising a diffractive optical element that includes fewer than ninephase levels.
 22. The lens of claim 16, wherein the axicon is affixed toa surface of the lens.
 23. The lens of claim 16, wherein the lens has anaspherical surface having the optical properties of a combination of aspherical surface with the axicon.
 24. The lens of claim 16, wherein thelens includes a doublet.
 25. The lens of claim 16, wherein the lensincludes a Cook triplet anastigmat.
 26. The lens of claim 16, whereinthe lens includes a symmetric double Gaussian.
 27. The lens of claim 16,wherein the MTF of the lens is higher with the axicon than without theaxicon for bar code symbols having spatial wavelengths of 10-20 mils,inclusive.
 28. The lens of claim 16, wherein the MTF of the lens is atleast 0.2 for a 10 mil bar code symbol that is from about 4 to about 16inches away from the lens.